vmatrix2.dat

basic linear algebra classes and applications (SVD,interpolation, multivariate optimization)

./vmatrix2


-------------------------------------------------------------------------------
		Verify Advanced Operations on Matrices

---> Verify determinant evaluation
for a square matrix of size 20

Check to see that the determinant of the unit matrix is one
	determinant is 1
Check the determinant for the matrix with 2.5
	at the diagonal
	determinant is 9.09495e+07
Check the determinant of the transposed matrix
swap two rows/cols of a matrix and watch det's sign
Check the determinant for the matrix with 2.5
	at the anti-diagonal
Check the determinant for the singular matrix
	defined as above with zero first row
	determinant is 0
Check out the determinant of the Hilbert matrix
    3x3 Hilbert matrix: exact determinant 1/2160 
                              computed    1/2159.99
    4x4 Hilbert matrix: exact determinant 1/6048000 
                              computed    1/6.04788e+06
    5x5 Hilbert matrix: exact determinant 3.749295e-12
                              computed    3.75127e-12
    7x7 Hilbert matrix: exact determinant 4.8358e-25
                              computed    6.54014e-25
    9x9 Hilbert matrix: exact determinant 9.72023e-43
                              computed    -1.10127e-39
    10x10 Hilbert matrix: exact determinant 2.16418e-53
                              computed    -3.15323e-47
Done

---> Verify matrix multiplications
for matrices of the characteristic size 20

Test inline multiplications of the UnitMatrix
Test inline multiplications by a DiagMatrix
Test XPP = X where P is a permutation matrix
Test general matrix multiplication through inline mult
Check to see UU' = U'U = E when U is the Haar matrix
Two (27,27) elements of matrices with values 1 and 1
differ the most, although the deviation 5.96046e-08 is small
Two (27,27) elements of matrices with values 1 and 1
differ the most, although the deviation 5.96046e-08 is small
Two (32,32) elements of matrices with values 1 and 1
differ the most, although the deviation 5.96046e-08 is small
Two (32,32) elements of matrices with values 1 and 1
differ the most, although the deviation 5.96046e-08 is small
Two (32,32) elements of matrices with values 1 and 1
differ the most, although the deviation 5.96046e-08 is small

Done

---> Verify vector-matrix multiplications
for matrices of the characteristic size 20

Check shrinking a vector by multiplying by a non-sq unit matrix
Check expanding a vector by multiplying by a non-sq unit matrix
Check general matrix-vector multiplication

Done

---> Verify matrix inversion for square matrices
of size 20

Test invesion of a diagonal matrix
Test invesion of an orthonormal (Haar) matrix
Two (5,4) elements of matrices with values 8.97181e-09 and 0
differ the most, although the deviation 8.97181e-09 is small
Two (5,7) elements of matrices with values 0.707107 and 0.707107
differ the most, although the deviation 5.96046e-08 is small
Test invesion of a good matrix with diagonal dominance
	computed determinant             4.69592
	determinant returned by invert() 4.69592
	check to see M^(-1) * M is E
Two (11,11) elements of matrices with values 1 and 1
differ the most, although the deviation 3.57628e-07 is small
	check to see M * M^(-1) is E
Two (11,11) elements of matrices with values 1 and 1
differ the most, although the deviation 3.57628e-07 is small

Done

All tests passed

Compilation finished at Fri Dec 25 23:09:17